Topic: Strength of Materials
Two shafts A and B are made of the same material. The diameter of shaft B is twice that of shaft A. The ratio of power which can be transmitted by shaft A to that of shaft B is
- A. 1/2
- B. 1/4
- C. 1/8
- D. 1/16
Answer: C. 1/8
Explanation: The power transmitted by a shaft is given by $P = \frac{2\pi NT}{60}$, establishing that $P \propto T$. The torque capacity of a solid shaft is $T = \frac{\pi}{16}\tau D³$, implying $P \propto D³$. The ratio of power transmitted by shaft A to shaft B is $\frac{P_A}{P_B} = \left(\frac{D_A}{D_B}\right)^3$. Given $D_B = 2D_A$, the ratio evaluates to $(1/2)^3 = 1/8$.